Question: If $x \odot y = 4x^{2}-y^{2}$ and $x \triangleleft y = xy+4x-y$, find $(2 \triangleleft -6) \odot 3$.
First, find $2 \triangleleft -6$ $ 2 \triangleleft -6 = (2)(-6)+(4)(2)-(-6)$ $ \hphantom{2 \triangleleft -6} = 2$ Now, find $2 \odot 3$ $ 2 \odot 3 = 4(2^{2})-3^{2}$ $ \hphantom{2 \odot 3} = 7$.